2010/02/01 by Josep Rifà, Rifà, Josep, Victor Zinoviev +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.DM #cs.IT #graph theory and CDMA systems #math.CO #math.IT
paper · pdf · doi:10.48550/arxiv.1002.0295
Submitted to IEEE Transactions on Information Theory
arxiv created 2010/02/01 · openalex publication_date 2010/02/01 · arxiv updated 2015/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider completely regular codes, obtained from perfect (Hamming) codes by lifting the ground field. More exactly, for a given perfect code C of length n=(qm-1)/(q-1) over Fq with a parity check matrix Hm, we define a new code C(m,r) of length n over Fqr, r > 1, with this parity check matrix Hm. The resulting code C(m,r) is completely regular with covering radius R = minr,m. We compute the intersection numbers of such codes and, finally, we prove that Hamming codes are the only codes that, after lifting the ground field, result in completely regular codes.